Question

if a and b are the measures of two first quadrant angles and sin a = 4/5 and sin b = 5/13, find sin a+b.

Answer 1

given that sin a= 4/5
cos a= √(1-sin²a)
         = √(1-16/25)
         = √(9/25)
         = 3/5
sin b=5/13
cos b= √(1-sin²b)
         = √(1-25/169)
         = √(144/169)
         = 12/13

sin(a+b)= sin a· cos b + cos a · sin b
              = 4/5· 12/13 + 3/5· 5/13
              = 48/65+15/65
               = 63/65
hope it helps

Answer 2

Answer:

[A]  sin(a + b) = $\frac{63}{65}$